My DS is also 15m. He drinks 1-2 cups of water a day, on average, plus nursing twice a day, but I try to always make sure he has a full cup available to him, both in his crib and in the playpen, in addition to at meals. I don't force the issue; he'll drink if he's thirsty and won't if he isn't.

If your DD is getting fussy and downing a whole cup of water when it's offered, have you tried just making sure there're cups around for her and see what she does with them?